NATIONAL UNIVERSITY OF SINGAPORE. Imaging FCS. A plugin for ImageJ. Thorsten Wohland August 17, 2015

Transcription

1 NATIONAL UNIVERSITY OF SINGAPORE Imging FCS A plugin for ImgeJ Thorsten Wohlnd August 17, 015 Imging_FCS 1.45 is bsic ImgeJ plugin to clculte nd view sptio-temporl correltion functions from 16 bit GRAY TIFF STACK files. It ws written under FIJI (ImgeJ 1.50; Jv 1.6.0_4) using the mth librry commons-mth nd requires Apche poi-3.11 for file reding nd writing. It clcultes correltions for ech pixel or group of pixels in the imge long the time xis (which is the z-xis in the stck). It contins wide rnge of functions including, blech correction, point spred function (PSF) clibrtion, clcultion the men squre displcement, mong others.

2 1 Imging FCS: A plugin for ImgeJ Contents 1. Introduction.... Clculting Correltions Dt Fitting Dul-Colour Fluorescence Cross-Correltion Spectroscopy (DC-FCCS) Clibrtion of the lterl Point Spred Function (PSF) FCS diffusion lw Men Squre Displcement - MSD Dt tble Sving nd loding dt Btch Mode Exiting the plugin Checking Progress Theoreticl ACFs nd Simultions Known Issues Recent Chnges to Imging FCS Acknowledgements Annex 1: Control Pnel ImFCS Element Annex : Fitting Functions Annex 3: Men Squre Displcement Annex 4: Simultion References... 39

3 Imging FCS: A plugin for ImgeJ 1. Introduction Wht does Imging FCS 1.45 do? Imging FCS 1.45 is n ImgeJ plugin tht llows clculting sptio-temporl uto- nd crosscorreltions of n imge stck (16 bit gry vlue TIFF). It cn perform the following tsks: 1. Clcultion of the temporl utocorreltion function (ACF) either t ech pixel (or squre res produced by n n binning) of n imge. Or t ny selected region of interest (ROI).. Clcultion of the sptio-temporl cross-correltion function for ny two pixels (or squre res produced by n n binning or mnully selected ROIs) of n imge. This cn lso be used for dul-colour fluorescence cross-correltion spectroscopy (DC-FCCS) if the imge is split on the cmer ccording to wvelength (fit models for both cses re provided). 3. Perform different blech corrections of the dt. 4. Anlysis of the correltions by fitting with the pproprite fit function (1). The progrm cn fit uto-correltions, sptil cross-correltions (diffusion nd trnsport), nd dul-colour cross-correltions. We provide simple non-liner lest squres or more time consuming generl lest squres lgorithm. 5. Clculte Model probbilities of fit functions using Byesin Model Selection (-4). 6. Pixels cn either be correlted or fitted individully using the mouse or keypd s selector. Or ll correltion functions in region of interest (ROI) or the whole imge cn be clculted utomticlly, possibly using n intensity filter to select to correlte only those pixels tht fll into certin intensity rnge. 7. Possible fit models, with mnully chosen prmeters, cn be visulized. 8. Depiction of prmeter mps (e.g. Diffusion coefficients, number of prticles, flow velocities, vlues) from the fit results. 9. Cretion of histogrms for the fit prmeters. 10. Production of sctter plots of fit prmeter pirs to check for correltions nd trends in the fit prmeters. 11. Clibrting the point spred function (PSF) by using freely diffusing smple (5). 1. Clculting the FCS diffusion lw for n FCS imge (6). 13. Produce dccf plots (dccf or CCF: difference between forwrd nd bckwrd correltion functions between neighbouring pixels; (1, 7)). 14. The men squre displcement (MSD) cn be clculted from the correltion function. 1 This document does not explin the theory of correltion nlysis but is only concerned with the use of the Imging FCS plugin. For detils on the theory plese see the references.

4 3 Imging FCS: A plugin for ImgeJ 15. Sving of experimentl dt nd reding nd reconstitution of experiments. Since this version the sving of the dt is done in.xlsx files. 16. Imging FCS 1.45 now lso llows to simulte dt in D nd 3D. Plese note, Imging FCS does not clculte pure sptil correltions; ll correltions re lwys performed in time. 1. Wht progrms do you need nd which files re provided in this distribution? 1. You need functionl instlltion of ImgeJ, Fiji, or Micromnger (the plugin ws compiled under ImgeJ 1.50, Jv 1.6.0_4 (64-bit), using Apche Commons commons-mth mth librry ).. You need to downlod nd instll Apche POI poi-3.11 in the jrs folder of Fiji ( At the time of writing this ws the ltest stble relese. These files re require for writing nd reding.xlsx files. 3. You need the Imging_FCS_1_45.jr file. 4. We provide the jv source file for your informtion. However, s Fiji updtes reltively fst s the migrtion to ImgeJ is hppening, there cn be compiltion problems. But the.jr file should work. So we suggest using the.jr file. 5. We provide 1x1 pixels test file mesured on fluorescently lbelled lipid bilyer, which contins 0,000 frmes nd ws recorded with 1 ms time resolution. 6. And of course this documenttion. 7. If there re problems with loding/using imges form the plugin, plese switch SCIFIO off (see section 14. Known Issues). 1.3 Instlltion Imging FCS works under ImgeJ, FIJI, or Micromnger. In the rest of the document we refer only to FIJI s Imging FCS hs been written under FIJI. However, the sme pplies to ImgeJ nd Micromnger. To strt Imging FCS, instll Imging_FCS_1_45.jr in the plugins folder of FIJI. On PCs you find this under Fiji.pp/plugins. On Mcs, go to the ppliction folder nd control click the Fiji ppliction. Select Show pckge contents nd copy the Imging_FCS_1_45.jr to the plugins folder. Then lunch Fiji. You cn strt Imging FCS under the Plugins tb in FIJI. Note, if you wnt to compile the progrm yourself from the jv source code you will need to instll commons-mth in the jrs folder of Fiji (\Fiji.pp\jrs) nd possibly remove the older commonsmth3-3.. You cn downlod this jr file t In ddition, you will need to instll the Apche POI poi-3.11 in the jrs folder of Fiji. Poi-3.11 cn be downloded t

5 4 Imging FCS: A plugin for ImgeJ Other wys to strt Imging FCS (but which will require compiltion): 1. Drg the Imging_FCS_1_45.jv file onto the FIJI progrm icon or, if FIJI is lredy open, onto the FIJI control pnel. This will open Imging_FCS_1_45.jv in the script editor. Then press Run. The progrm will be compiled nd strted (not working on Mc nymore).. When in FIJI, press the smll letter l. This opens the Commnd Finder. Serch for the script editor. Strt the editor by double clicking it. Then open the Imging_FCS_1_45.jv file nd run it. The progrm will be compiled nd strted. Note: Do not instll the.jr file nd try running the jv file in Fiji t the sme time. This cn led to some errors in the execution. We suggest to just using the.jr file. 1.4 Strting the plugin nd loding imges After you strted the progrm, you will see the ImFCS control pnel: Fig. 1.1: ImFCS Pnel. The description of ll prmeters is given in Annex 1 Control Pnel ImFCS Elements. Note tht the title of the control pnel contins lso the nme of the imge (here tril4_test.tif ) which ws used t tht moment by the plugin Loding n Imge Click the Lod button on the upper right. A dilogue will pper tht will let you lod ny imge stck. Mke sure the imge stck you lod is 16 bit GRAY TIFF STACK file Use n existing Imge In cse the imge stck you wnt to nlyse is lredy open in FIJI, click on tht window to mke sure it is the uppermost window nd then click the Use button. The imge will then be resized nd plced long the ImFCS control pnel for further use Required Prmeters The plugin reds in the bsic informtion from the file, including the number of frmes, dimensions of the frmes (not shown in the plugin but shown by imgej), the bckground vlue (the lowest counts found in the entire stck). However, experimentl prmeters hve to be properly entered

6 5 Imging FCS: A plugin for ImgeJ for the fit informtion to mke sense. This includes the following: Frme time, Pixel Size, Mgnifiction, NA, Emission wvelength, lterl PSF, xil PSF. The definition of ll these prmeters is given in Annex 1. In the cse of two-colour mesurements, Emission wvelength, lterl PSF, xil PSF hve lso to be provided. The vlues for the xil PSF cn be obtined by mesuring the light sheet thickness (1/e vlue, see Annex 1). The lterl PSF cn be obtined by clibrtion mesurement nd using the Clibrte PSF function of the plugin (see section 5). 1.5 Strting multiple instnces of the plugin Fiji llows running multiple instnces of the sme plugin. This mens one cn run the Imging FCS plugin severl times nd in ech use different imge. To mke differentiting between the windows possible, ech window of the plugin crries its title plus the title of the imge loded. E.g., in Fig. 1.1 the control pnel is clled ImFCS. In Fig. 1., the nme tril4_test.tif hs been dded to yield ImFCS tril4_test.tif to indicte tht the control pnel uses the imge stck tril4_test.tif. The sme will be true for ll other windows (correltion functions, prmeter mps etc.). The To Front button of the plugin llows bringing ll windows connected to tht pnel to the front. Fig. 1.: After selecting file with Use Imge or Lod imge, the selected imge is djusted in size nd plced longside the ImFCS Pnel. The ImFCS pnel is renmed to contin the imge nme.. Clculting Correltions.1 Performing individul correltion nlysis After the imge stck is loded perform one of the three following ctions to clculte the correltions s specified within the Control pnel (for detils on the different options see below): 1. Use the mouse to click ny pixel within the imge nd the progrm will clculte nd depict the correltion, stndrd devition, nd intensity trce.. Enter the desired pixel coordintes in the text fields for Pixel X nd Pixel Y in the control pnel nd click the Single button on the lower left.

7 6 Imging FCS: A plugin for ImgeJ 3. If you hve number pd, you cn use the, 4, 6, nd 8 keys to move within the imge (the number or cursor keys don t work s they hve lredy other uses in FIJI). You should see the correltion nd intensity trce windows s on the left in Fig. 3. In ddition, the stndrd devition (SD) of the utocorreltion function is depicted. The SD cn be clculted in different wys (see more under. Blech Correction). It cn be directly clculted during the computtion of the ACF. As the ACF is the men vlue of mny individul intensity/photon count products, the stndrd devition of the ACF is clculted s the stndrd error of the men of these products (8) nd is then corrected by blocking procedure (3). Correltion function from rw dt Sliding window correction Fig..1: Correltion functions nd intensity trce. On the left the correltion is performed on the rw dt. On the right side sliding window blech correction hs been pplied. Note tht the intensity trce is the sme (for more informtion see the text). The stndrd devition in the lower pnels is the stndrd devition clculted for the correltion functions.. Blech Correction If bleching is present, the dt cn be corrected by one of three methods. Either sliding window pproch cn be used. In this cse, the totl intensity trce for ech pixel is divided into subsets. The

8 7 Imging FCS: A plugin for ImgeJ correltion is then performed on ech subset nd the results re verged. Note, tht this will reduce the overll time vilble for correltions (the correltor P nd Q vlues re utomticlly djusted by the progrm) nd increse the vrince especilly t long times mking fitting of slow prticles nd possibly G, i.e. the correltion vlue t long times, more difficult. As defult, the trces re divided into 0 subsets. However, the sliding window size, nd thus the number of subsets of the intensity trce, cn be chnged in the Sl Win Size field in the ImFCS Pnel. The pnel on the right in Fig. 3 shows the ACF of the left pnel fter sliding window blech correction. Note tht the SD chnges ccordingly. However, the intensity trce stys the sme s it is not corrected. Note: If the sliding window is nrrow nd cnnot cover enough time to llow the clcultion of full correltion function, then the results of the fits will be bised (6). Single exponentil blech correction Double exponentil blech correction Fig..: Single nd double exponentil blech corrections. The dt is the sme s in Fig. 3 for comprison of the three blech correction pproches. In ddition to the sliding window pproch, the dt cn lso be corrected by single or double exponentil fit to the intensity trce (see Fig..). In tht cse the intensity trce is corrected by single or double exponentil fit, which is reflected in the chnge of the intensity trce plot. The dt chosen for Fig.. is the sme s for Fig..1 for better comprison.

9 8 Imging FCS: A plugin for ImgeJ The sliding window pproch cn tke ccount of generl slow fluctutions, nd not only blech decys, nd provides dt which is very similr to the exponentil fits if only bleching is present. However, s it uses subsets of the totl mesurement it cn led to distortions nd bises of results (9) if the subsets re too smll. So sliding window pproches should be used for long dt sets nd for sets which show chnges other thn just bleching..3 Performing nlysis of regions of interest or the whole imge To clculte ll correltions simultneously click the button All on the lower right. It will tke less thn 0 seconds to clculte ll correltions for 0x0 imge. Lrger or smller imges will tke less or more time ccordingly. Note tht now the intensity trce shows the verge intensity of the whole imge: Fig..3: All correltions clculted for 1x1 pixels imge. Here sliding blech correction ws used. It took ~ 8 seconds for the clcultion of ll ACFs. The intensity trce is now he verge intensity for the whole imge. Below the All button you cn chose possible filter. The defult is none. If you chose Intensity or Men, you will be sked to provide upper nd lower thresholds for the intensity (of the first frme) or for the men intensity vlue. The filter dilogue will pop up ech time you press All button Only pixels whose intensity/men intensity flls between these thresholds will be correlted. This feture is useful if one wnts to void fitting bckground pixels. This speeds up the clcultions nd reduces fitting problems s bckground pixels hve no correltions nd the fit will return meningless vlues (nd sometimes cn hng the progrm). Fig..4: Selection of lower nd upper threshold for pixel intensities/men intensities s selection filter for which pixels ought to be correlted.

10 9 Imging FCS: A plugin for ImgeJ The sme procedure cn be pplied to regions of interest (ROIs). Just select ROI in the imge by using the ROI tools of FIJI nd then press the button ROI. Filters cn be set in the sme wy s for the All buttton..4 Difference in cross-correltion functions (CCF or dccf) The difference in cross-correltion functions (CCF or dccf) is the integrted difference between the forwrd nd bckwrd correltion functions between two sptilly different res. It contins informtion bout ctive trnsport of molecules nd smple heterogeneity (1, 5, 7): T CCF CCF CCF 0 AB BA d In the cse of diffusion the men vlue of the dccf is close to 0. In the cse of flow or ctive trnsport the dccf is positive or negtive depending on the dccf direction nd the flow/trnsport direction. The width of the distribution is mesure of the heterogeneity. Fig..5: dccf imge clculted in the x direction. Note tht the dimension of the originl imge ws 1x1 pixels. But s the dccf hs been clculted in the x direction it contins now 0x1 pixels only. On the right side the dccf histogrm is shown. 3. Dt Fitting 3.1 The Fit pnel To fit the dt press the Fit button. This is toggle button tht switches dt fitting on or off. When switched on Fit prmeter window is shown which crries the title ImFCS Fitting :

11 10 Imging FCS: A plugin for ImgeJ Fig. 3.1: Fit prmeter window ImFCS Fitting. There re now two possibilities for fitting dt. One cn use either weighted non-liner lesed squres (NLS) fit or generlized lest squres (GLS) fit. One cn chose between the two by switching the GLS button on or off. The NLS fit is weighted fit, where the weight is given by the stndrd devition (SD) of the correltion functions. The SD is now clculted by the blocking trnsform (3). For the GLS fit the covrince mtrix is clculted from the blocked correltion dt nd is regulrized ((3) nd references therein). If the button Byes is switched on then the progrm fits one- nd two-component model 3 to the dt nd clculted the model probbilities of ech model. The results will be given in the Byesin Model Probbility section t the bottom. The Test button llows to drw theoreticl correltion function with the prmeters s provided in the fit window. So one cn djust these prmeters mnully nd see how they chnge the correltions function. We hve introduced Set nd Free/Fixed button. The set button sets the current fit prmeters s fixed nd ll fits lwys strt with these fit prmeters. Ech time the set button is pressed the fit prmeters re set new to the current vlues. To undo tht the Free/Fixed button cn be clicked. If it is set to free, then ech fit strts with the resulting fit prmeters from the lst fit. This is useful where the correltion functions hve trend to shift over the imge so tht the first nd lst pixel hve very different vlues but there is smooth trnsition for the pixels in between Note tht the vlues for, w, rx, nd ry re clculted from the prmeters given in the ImFCS Pnel nd they cnnot be edited by the user. If these prmeters need to be chnged, chnge the prent prmeters (Pixel size, mgnifiction, lterl PSF (xy), Em. Wvelength, NA, binning, CF X distnce, CF Y distnce) in the ImFCS Pnel. 3 More models nd the control over which models will be used in the Byesin Model Selection will be dded in future versions.

12 11 Imging FCS: A plugin for ImgeJ The definition of these prmeters re expline here: Fit Model: This cn be either FCS or DC-FCCS GLS Fit: Switch between weighted NLS or GLS fits. [nm]: pixel size in imge spce, defined s Pixel size/mgnifiction w [nm]: 1/e rdius of the lterl PSF. This is clculted from lterl PSF (xy) * Em. Wvelength / NA rx [nm]: Distnce in x direction between pixels to be correlted. This is clculted from CF X distnce * Pixel size * binning / mgnifiction ry [nm]: Distnce in y direction between pixels to be correlted. This is clculted from CF Y distnce * Pixel size * binning / mgnifiction rz [nm]: This is possible shift of the two light sheets ginst ech other in DC-FCCS. This is qulittively different from the rx nd ry vlues which just describe the distnce of the pixels to be correlted. rz ccounts for possible mislignment of the light sheets in z-direction. Fit prmeters: All fit prmeters cn be either free or fixed (see the rdio buttons clled hold ). By setting certin prmeters to 0 nd clicking hold t the sme time, one cn use different fit models (diffusion only, flow only, diffusion nd flow, one component, two components etc.). N: Number of prticles in observtion re or volume. Note tht this prmeter mkes no strict sense in terms of prticle numbers for sptil cross-correltions. G: Convergence vlue of the correltion function for long times. This is expected to be 1. Devitions from 1 cn indicte problems with bleching. After blech correction this vlues should be close to 1. D, D, D3: Diffusion coefficients of species 1, nd 3. vx nd vy: flow speeds in x nd y directions. If no flow is to be fitted, they cn be set to 0 nd put on hold. Note, t the moment only one flow component (vx, vy) is llowed. So it is ssumed tht even if severl prticle species re present, they cn hve different diffusion but hve the sme flow. F, F3: Frction of species or 3 if present; one cn set these selectively to 0 nd put on hold for one-, two-, or three-component fits. The frction of species 1 is F1 = 1 F F3. Q, Q3: This is the brightness of the second nd third prticle in respect to the first prticle. For proper fit this needs to be known nd the correct vlues hve to be entered here. E.g. if the second prticle is 50% brighter, this vlue hs to be set to 1.5. If the vlue is set incorrectly the fit will give wrong vlues for F. The sme is true for Q3 nd F3. If one of the components is set to 0 (F = 0 nd put on hold) then the corresponding Q prmeter hs no influence.

13 1 Imging FCS: A plugin for ImgeJ After the prmeters hve been set one cn then click on ny pixel in the window or use the Single button in conjunction with the coordintes in the text fields Pixel X nd Pixel Y to obtin the correltions nd the fit. When fit is performed, the residuls will be plotted in n dditionl window below the intensity trce window. After fitting the function for one pixel you should see the following: Fig. 3.: Dt fit. The progrm shows now the fit with the correltion function in the Correltion Function Disply nd cretes residuls plot. In ddition, new stck window with prmeter imge mp will be opened s described in the next section. If the ROI or All button is pressed ll relevnt pixels re correlted nd then fitted. Which pixels re fitted depends on binning nd whether one uses utocorreltions, sptil cross-correltions, or dul-colour cross-correltions, nd whether overlp is switched on or off. It is importnt tht before pressing the ROI or All button you check tht you hve sensible fit prmeters in the Fit pnel s they will be used s strting vlues. If the prmeters re too fr off, fitting cn longer nd might result in mny pixels without fits s fits might not converge. If fits don t converge log window will be opened with messge giving the pixel t which problems were encountered nd wht the problem ws 4. For membrne diffusion, good strt is mostly N = 1, D = 1 m s -1, nd G = 1 (ll three free) nd ll other vlues 0 nd on hold. You cn refine models nd prmeters subsequently. The correltion tkes bout 40 seconds for 0x0 pixel imge with 50,000 frmes (McAir 1.7 GHz Intel Core i5). 4 We hve limited itertions nd evlutions to 000 in the progrm s tht ws good compromise nd reching fits for the most number of pixels without tking too much time for the fit. This cn be chnged in the jv file by chnging the vribles fitmxitertions And fitmxevlutions.

14 13 Imging FCS: A plugin for ImgeJ 3. Binning nd Overlp mode When binning is used, n n pixels will be dded together before the correltion is clculted. Binning cn be used to provide better signl in some cses. In the cse of binning the user cn decide between two modes, overlp nd non-overlp by selecting the Overlp On/Off button. In overlp mode neighbouring pixels will overlp while in the non-overlp mode only non-overlpping pixels will be clculted nd correlted. The dvntge of the overlp mode is tht it provides more correltion functions nd tht correltion functions cn be clculted for ny position nd ny binning on the imge. The non-overlp mode lwys strts with the left upper most imge point nd thus llows only certin pixels to be defined. At the moment the progrm llows only squre binning, i.e. n n binning. Fig. 3.3: Explntion of Overlp mode. In the upper pnel four pixels for 3 3 binning in non-overlp mode re shown. In the lower pnel the 4 pixels re shown in overlp mode. 3.3 Prmeter Mps nd the Histogrm Window If fit is selected nd correltion is clculted new stck window with prmeter imge mp will be opened nd histogrm window for the prmeters will be creted. The prmeter mp window is new stck window tht contins s mny mps s there re prmeters plus mp of the vlues for ll fits, nd n dditionl mp indicting whether blocking ws succesful for the clcultion of the stndrd devition (3) 5. Using the scrollbr t the bottom one cn switch between the different prmeter mps. In the histogrm window the corresponding histogrm to the selected prmeter mp is shown. However, histogrms re shown only for the free fit prmeters (including ). The number of bins in the histogrm re clculted by the Freedmn-Diconis rule (10): number _ of _ bins 3 number _ of _ dt _ points Mx Min Inter _ Qurtile _ Rnge Here is the mp for the number of prticles N shown (in this cse ll correltion functions hve been fitted to show full mp). The title contins the nme of the prmeter plus its men nd stndrd devition. 5 If blocking is not successful, i.e. the stndrd devition does not converge to stble vlue, this typiclly indictes tht the mesurements weren t sufficiently long nd noise correltions exist for times longer thn the correltion times. In this cse so-clled mximl blocking will be used s described in the cited rticle.

15 14 Imging FCS: A plugin for ImgeJ Fig. 3.4: Prmeter nd histogrm window. If single fits re performed, the dt of these single fits will be updted in these mps. This is useful if some of the btch fits re not good nd hve to be individully refitted. Note: If the fit prmeters for one of the pixels re required, click on tht pixel in the prmeter mp window. The fitted prmeters will then be displyed in the ImFCS Fitting pnel, nd the correltion function nd its fit will be shown in the correltion function window. Here we show the cse in which ll correltion functions hve been clculted nd fitted. Note tht the progrm clcultes the correltions ech time new, so tht ny chnges in prmeters in the control pnel re tken into ccount. The exception here is binning s in this cse the whole mp needs to be chnged. The combined correltion nd NLS fit tkes bout 45 seconds for 0x0 pixel imge with 50,000 frmes. The sme with GLS fit tkes bout 45 minutes. Note: If binning is chnged, ll existing fit results re discrded, s the progrm t the moment does not support the use of different binning simultneously. You cn remove single fits from the evlution by double clicking tht pixel in the prmeter mp. This removes ll fit vlues nd correltions but not the rw intensity dt in the imge. By clicking the sme pixel in the imge the correltion nd fit cn be done gin. 3.4 Sctter Plots Imging FCS llows depicting sctter plots of prmeters ginst ech other. This is useful to check for correltions between prmeters. Correltions between prmeters cn be sign of problems in the fit (e.g. the frction nd chrcteristic time cn sometimes be correlted if the dt is not sufficient to distinguish between two different prticles/processes). But more importntly the correltion cn lso stem from the smple. E.g. the diffusion coefficient nd number of prticles cn be correlted when in res where there the concentrtion of prticles is high re lso res where the prticles interct/bind or the density is higher. The progrm llows the depiction of 7 different sctter plots: N vs D, N vs F, D vs F, N*(1- F) vs D, N*F vs D, D vs (v x +v y ) nd D vs (v x +v y ).

16 15 Imging FCS: A plugin for ImgeJ Fig. 3.5: Sctter Plot exmple of N vs D. 3.5 Recommendtions for fitting We tested the weighted NLS nd the GLS fits on simultions. Both fits need minimum number of frmes to converge to the simulted diffusion coefficient. This is bout 50,000 fres for the NLS fit nd somewht longer for the GLS fit. However, for the sme number of frmes the GLS fit will hve n bout 30-40% smller stndrd devition for the diffusion coefficient. But the GLS fits tke much longer. Therefore, we suggest to use the NLS fit for initil evlutions nd then use the GLS fit only in the lst step. A comprison between the diffusion coefficient of the NLS nd GLS fit will then tell whether both converged to the sme vlue. Byesin Model Selection uses GLS fits nd fits multiple models. So it will tke correspondingly longer nd probbly should be used only in the finl evlution. In future versions we will try to speed up the clcultions. 4. Dul-Colour Fluorescence Cross-Correltion Spectroscopy (DC- FCCS) DC-FCCS mesurements ssume tht the imge ws split ccording to wvelength onto two prts of the imge sensor. For DC-FCCS mesurements, plese switch the fit model in the Fit Model field in the control pnel to DC-FCCS. The distnce between the green nd red pixels hs to be provided in the CF X distnce nd CF Y distnce fields of the control pnel. Clicking onto ny pixel within the green chnnel (green shded re in Fig. 4.1) will then provide the cross-correltion function in the Correltion plot window. If one wnts to depict both ACFs nd the CCF simultneously, one cn switch on the toggle button "FCCS Disply". If this button is set on On, the cross-correltion is plotted in blue nd the ACFs in green nd red. Switching on FCCS lso utomticlly switches the fit model to the DC-FCCS model. For the clcultion of multiple DC-FCCS functions, chose ROI in the region of the green chnnel, set the CF X distnce nd CF Y distnce nd then press ROI.

17 16 Imging FCS: A plugin for ImgeJ Fig. 4.1: On the left is shown the principle for DC- FCCS. The green nd red shded res represent the imges split ccording to wvelength on single rry detector. The user hs to provide the distnces between the green nd red pixels. The progrm cn clculte the cross-correltion between the corresponding pixels then. Importnt: Of course DC-FCCS cn lso be clculted for ll relevnt pixels with fitting. However, you should first mke sure tht there re cross-correltions. Otherwise, clcultions cn tke long, s the fits do not converge, nd mny fits will not provide fitting prmeters. In ddition, mke sure tht the strting vlues in the Fit pnel re sensible (e.g. no negtive numbers). If the strting vlues re too fr off, the fits will not converge (see lso 3.1 Fit Pnel). Plese lso note tht the FCCS Disply mode is set to off if the All button is pressed s tht results in too mny curves to be plotted within one grph. In tht cse only ll cross-correltion curves re plotted, with their fits, if pplicble, without the utocorreltions. Fig. 4.: Crosscorreltion disply in dul colour mode. 5. Clibrtion of the lterl Point Spred Function (PSF) The progrm requires the xil dimensions of the PSF in the field xil PSF [um] in the ImFCS control pnel. The xil dimensions, i.e. the 1/e rdius of the light sheet, needs to be mesured nd

18 17 Imging FCS: A plugin for ImgeJ provided. If D correltion is desired, the vlue cn be set to lrge number (the defult is ) in which cse the thickness plys no role in the correltion nd essentilly D fit is performed (e.g. for imging totl internl reflection FCS or ITIR-FCS). Once tht is entered the user cn press the Clibrte PSF button nd smll dilog will pper. This will sk the user first for rnge of PSF vlues to be used (strt vlue, end vlue, step size). Fig. 5.1: PSF dilog. Typiclly one should not use more thn 5 prmeter vlues t the sme time s the clcultion cn become slow (e.g. Strt 0.7, end is 1.1, step size 0.1). The progrm will then plot the diffusion coefficients fitted by simple one component model to the smple for binning vlues from 1-5. As the diffusion coefficient is constnt the correct PSF vlue should led to stright line. Fig. 5.: Plot to determine the PSF size. 6. FCS diffusion lw The FCS diffusion lw cn lso be clculted (5, 6). Pressing the button Diff. Lw in the control pnel will plot the FCS diffusion lw for n FCS imge. As this requires the clcultion of correltions over the whole imge severl times, this is bit slower thn e.g. fitting ll correltions in n imge. Note lso, tht blech correction cn be selected nd will be tken into ccount in the clcultions.

19 18 Imging FCS: A plugin for ImgeJ Fig. 6.1: Diffusion lw plot. Note tht the results of the diffusion lw plot re given bove the frme, here the line ws best fit by *Aeff. 7. Men Squre Displcement - MSD When the MSD button is switched on, then the MSD is directly clculted from the ACF (11) for the prt of the ACF t which its vlue is t lest 90% of its mplitude. This mens the MSD is only clculted for the first points up to bout the diffusion time (i.e. the time prticle needs to cross the observtion volume). When switching MSD on, dilogue will pper nd request whether D (ITIR-FCS) or 3D (SPIM-FCS) MSD clcultions re required. Note tht for 3D (SPIM-FCS) MSD clcultions, the sigmz in the IMFCS pnel hs to be provided, otherwise fit error will be produced. Fig. 7.1: MSD dilogue The MSD is clculted by inverting the ACF. As this is non-trivil for the Error Function, this is done numericlly (see Annex 18). No fitting procedures re provided s yet but the dt is sved in the experimentl.xlsx files. Fig. 7.: MSD plot clculted from correltion function of DOPC bilyer.

20 19 Imging FCS: A plugin for ImgeJ 8. Dt tble The dt cn be visulized in dt Tble by pressing the Tble Crete/Updte button. The dt tble is not utomticlly updted. The tble cn be updted by pressing gin the Crete/Updte button. Fig. 8.1: Dt tble. The first tb contins the pnel prmeters. The other tbs contin the numericl vlues of clcultions nd fits. The dt in this tble is the sme tht is sved in the.xlsx files. 9. Sving nd loding dt Since this plugin version ll dt is sved in.xlsx files. Imging. This provides spredsheet formt which cn be red by mny other progrms nd fcilittes the trnsfer of the dt to different progrms. Note: s we hve chnged the file formt for sving, this plugin is NOT bckwrds comptible to erlier versions nd experiments sved in versions 1.3 nd erlier cnnot be red. When pressing the button Sve dilog will open sking the user which dt to sve: Note: To open n experiment the imge for tht experiment hs to be lredy loded, otherwise the progrm will no recrete the experiment! Fig. 9.1: File selection window.

21 0 Imging FCS: A plugin for ImgeJ 10. Btch Mode In btch mode, dilogue window will be opened (Fig. 8.1) which llows the user to select which clcultions re to be performed. In ddition, suffix text field llows the user to specify suffix tht will be dded to the imge file nme to crete the new output file nme for the.xlsx file. If no suffix is specified the plugin dds the dte nd time to the imge file nme to crete unique filenme for sving. For instnce if n imge file is clled bilyer.tif nd you specified the suffix -evluted, then the output filenme will be bilyer-evluted.xlsx. If you did not specify suffix nd ssuming the progrm ws run on My 11, 015 t 10:30:1 (h:m:s), the output file will be nmed bilyer015_05_11-10_3_1.xlsx. After this selection n Open Dilog Window will be displyed (Fig. 8.), which llows the user to select multiple files to be treted in the btch mode. Note tht t the moment only files cn be selected, no directories. Fig. 10.1: Btch processing dilog. The resulting.xlsx files re sved in the sme directory s the imge files. Fig. 10.: The Open Dilog Window for Btch processing.

22 1 Imging FCS: A plugin for ImgeJ 11. Exiting the plugin Press the Exit button nd the plugin will be terminted nd ll windows nd dt will be removed. 1. Checking Progress Progress for ll clcultions is shown in the ImgeJ sttus br. It is given s progress br nd short messge wht is being done (here: Correlting ll pixels ). Fig. 1.1: Progress is indicted by progress br including short messge bout wht is being done. 13. Theoreticl ACFs nd Simultions The plugin llows to plot theoreticl FCS functions or to simulte D diffusive system ( 3D version is plnned for lter). By pressing the Test button in the Fit pnel (see Fig. 3.1) the theoreticl ACF with the prmeters form the fit pnel will be plotted in the Correltion Function Disply window. This cn be useful to obtin estimtes for initil prmeters or in generl to get feeling for the chnges of ACF functions with prmeters. The button Simultion in the control pnel will bring up dilog with djustble prmeters for simultion (for detils see Annex 4). A simultion for 100,000 frmes with 0x0 pixels nd 400 simulted prticles tkes bout 40 seconds to run. The simultor cretes n Imge which is utomticlly set s the ctive window for the plugin. All opertions of the plugin cn be pplied to this imge. 14. Known Issues 1. In Micromnger use ImgeJ version 1.47v or lter (which come with Micromnger version nd lter). In erlier Micromnger versions nd , which re bundled with erlier versions of ImgeJ, the progrm cn be slow or possibly does not support the output of plots.. In the ImgeJ updte from June 014 (ImgeJ.0.0-fc-SNAPSHOT) switch SCIFIO off for loding imges. This does not work properly with the plugin. You cn do tht under the menu item Edit/Options/ImgeJ nd then mke sure tht the option Use SCIFIO when opening files is not ticked.

23 Imging FCS: A plugin for ImgeJ 3. If Fit is switched on but the dt cnnot be properly fit, it cn hppen tht FIJI stops responding, which then requires to stop FIJI (tsk mnger on PC, or Force Quit on Mc). This problem hs now been mitigted by limiting the fit to 000 itertions nd evlutions ech nd by running ll correltions nd fitting on bckground thred in jv. The progrm will now open FIJI log window nd reports ll pixels t which fitting exceptions occurred. 4. If the plugin/.jr file cretes error messges when strted, check tht you run ImgeJ 1.50 or higher. 14. Recent Chnges to Imging FCS 14.1 Chnges from 1.43 to The ACF fits were mde considerbly fster (see typicl performnce vlues s given on the website).. A bug ws corrected which led to repeted pop-up windows if prmeters were set out of relistic bounds for the fits. If prmeters re unrelistic there is now single messge nd the fits re ll terminted. 3. The simultions were improved to contin more options nd new pnel. 4. A bug in the disply of dccf functions when using pixel binning ws corrected. 14. Chnges from 1.4 to The simultor ws upgrded nd llows not D nd 3D simultions.. The prmeter mps re now set overll to NN so tht the sttistics of the histogrms tkes only ccount of the ctully fitted vlues. Therefore the verge vlues in the title of the prmeter windows hve been removed. 3. Clicking pixel in the prmeter window now updtes ll windows including the intensity nd residul windows. 4. One cn now remove single fitting nd correltion results by double clicking on pixel in the prmeter mps. 5. Singulr Mtrix Error messges re not nymore displyed. The fit is unsuccessful nd the vlues in the prmeter windos re set to NN (not number). 6. The liner fit for the diffusion lw is now weighted correctly with the vrince (before it ws weighted with the stndrd devition).

24 3 Imging FCS: A plugin for ImgeJ 14.3 Chnges from 1.41 to An FCS simultor ws included. However, t the moment it is restricted to D diffusion Chnges from 1.4 to Bug fixes regrding the clcultion of some of the res for ROIs nd the cretion for irregulr ROIs for the sptil cross-correltion.. MSD ws originlly clculted only for D smples, i.e. for ITIR-FCS. MSD is now lso clculted for SPIM. 3. Documenttion ws corrected, s in the SPIM function fctor 4 ws missing in the lst term Chnges from 1.3 to The progrm now sves ll dt in the.xlsx spredsheet formt nd reconstitutes experiments from these files. Note tht now older experiments sved with versions 1.3 nd erlier cnnot be loded with this plugin nymore.. The men squre displcement (MSD) cn now be directly clculted from the correltion function (D diffusion only t the moment). 3. A Dt tble file cn be creted to visulize the numericl vlues of the results. 4. Multiple bugs relting to the depiction of the FCCS functions were corrected. 5. Overlp mode cn now lso be used for the clcultion of diffusion lws. 6. Additionl blech correction modes were dded. 7. NullPointerExceptions tht crept up with one of the recent Fiji updtes were corrected Chnges from 1.9 to The progrm llows now lso to clculte correltions nd fits in region of interest (ROI). Just select ny region of interest nd click ROI in the pnel to obtin the correltions.. The FCS fit model ws updted to hve now up to 3 diffusing components. While this is of limited use s the Imging FCS dt (or ny other FCS dt for tht mtter) does typiclly not hve sufficient S/N to resolve 3 components, it cn be useful for comprison in Byesin Model Selection. Note tht the FCCS model contins still mximlly components.

25 4 Imging FCS: A plugin for ImgeJ 3. The FCS model hs been corrected s there ws n error in the clcultions of the derivtives for the frction of the second component. This however did not ffect ny one component fits done up to now. 4. Fitting: Note tht we do not support nymore non-weighted fits. We hve introduced two new options in fitting, GLS nd Byes. If both re off, fits re performed by weighted non-liner lest squres fitting. If Generlized Lest Squres (GLS) is on then fits tke the covrince mtrix into ccount nd not only the vrinces. The fits however tke much longer. So for initil evlutions we still recommend to use the norml weighted fits. If Byes is on then multiple models (t the moment only 1 nd component models; in the future we will introduce options to select nd include more models) re fit nd the likelihood of ech model is provided. Byes works with nonliner lest squres nd lso with GLS. 5. In the Fit pnel we hve introduced Set nd Free/Fixed button. The set button sets the current fit prmeters s fixed nd ll fits lwys strt with these fit prmeters. Ech time the set button is pressed the fit prmeters re set new to the current vlues. To undo tht the Free/Fixed button cn be clicked. If it is set to free, then ech fit strts with the resulting fit prmeters from the lst fit. This is useful where the correltions functions hve trend to shift over the imge so tht the first nd lst pixel hve very different vlues but there is smooth trnsition for the pixels in between. 6. All correltions nd fitting is done now on bckground thred in jv. This llows the user to continue working while the clcultions re done. 7. A progress br is now indicted insted of the counting of clcultions to show the progress Chnges from 1.6 to A bug ws fixed in the sliding window blech correction which cused the correltion to be lwys clculted for sub-stck strting with slide 1 (irrespective of wht vlue ws entered in the field "First frme").. A bug in DC-FCCS ws fixed which ws preventing fitting of the ACFs in the red chnnel, cusing the progrm to bort clculting nd fitting the correltion functions. 3. Updting of window nmes ws introduced for ll output windows; when output windows re re-used for results of correltion of newly loded imge, their nmes re updted to mtch the nme of the current imge. 4. A bug ws fixed in creting prmeter mps in DC-FCCS; when x or y coordinte of the initil pixel of the green region ws lrger thn 0, the bug resulted in prmeters for only prt of the selected region being displyed in the mp, the rest of the pixels in the prmeter mp contining zeros. 5. In DC-FCCS, prmeter mps re shown for the cross-correltion s well s for the utocorreltions in both the green nd the red chnnel in the following order:

26 5 Imging FCS: A plugin for ImgeJ prmeters for cross-correltion, prmeters for green chnnel, prmeters for red chnnel, Chi of CCF fit, Chi of green ACF fit nd Chi of red ACF fit. 6. The fit model for diffusive components ws corrected s in the normliztion the denomintor ws not rised to the second power. This influenced if t ll only mplitude, no diffusion coefficients. 7. We introduced new Overlp toggle button. This is importnt for binning. Previously only non-overlpping binned pixels were llowed. In this version the user cn chose between overlpping nd non-overlpping pixels. 8. We introduced the blocking Trnsform (3) to clculte the stndrd devition of the ACFs. The blocked stndrd devition lso tkes ccount of the noise correltions nd should led to better fits. Whether blocking ws successful (nd thus the dt collection ws sufficient) is shown in n own pnel in the prmeter mps. It is lso sved long with the Fitting prmeters. 9. The exponentil blech correction hs been improved nd now conserves the verge nd vrince (1). 10. Fit prmeters nd fit functions cn now be re-clled by pressing on pixel in the prmeter mps. 15. Acknowledgements The progrm ws checked for bugs by different people in the lb, especilly Rdek Mchn nd Nirmly Bg. Rdek ws lso responsible for mny bug fixes in the newer versions nd work on the DC-FCCS prt. Jgdish Snkrn wrote the MSD clcultion lgorithm. Mrk Bthe nd Syun-Ming Guo wrote the first GLS nd Byesin Model Selection lgorithms in Mtlb ( nd they helped very ptiently with the coding of the lgorithm in jv. I m grteful for ll the help which improved the progrm considerbly. All remining errors nd bugs re entirely my fult, nd I will be grteful for ny feedbck or help in improving the progrm.

27 6 Imging FCS: A plugin for ImgeJ 16. Annex 1: Control Pnel ImFCS Element Use: Pressing the Use button will tell the progrm to use the uppermost imge window in ImgeJ for the correltions. This imge hs to be 16 bit grey vlue stck, otherwise the progrm will provide n error messge. If unsure which window is on top, you cn just click the window you wnt to use before pressing the use button. Lod: This button will open dilogue for loding n imge file, which is then used in ImFCS. Btch: Allows to evlute severl files with the sme options. First the user will be sked which evlutions to perform. Then the user will be sked to select one or multiple files. The files will then be sequentilly loded nd evluted nd the dt will be sved in.xlsx files (see section 8). First Frme: This is the first frme t which the correltor will strt. This prmeter is typiclly 1 but cn be chnged so tht the correltions will strt from ny frme you chose. This llows the user to nlyse correltions t ny time within the imge series. This might be importnt if the cmer hs n unstble bseline t the beginning of n imge series, or if there re ny other rtifcts t the strt of the imging series. Lst Frme: This is the lst frme the correltor will use. This prmeter is set to the lst frme of the loded imge. It cn be chnged if only prt of the stck is to be correlted. Frme Time: The user hs to provide the cquisition time per frme which ws used in the cquisition of the imge stck. This will influence the time xis nd the fit results. Binning: This llows binning multiple pixels into lrger pixel. At the moment ImFCS llows only squre binning (1x1, x, etc.).

28 7 Imging FCS: A plugin for ImgeJ CF X Distnce nd CF Y Distnce: If sptil cross-correltions re to be clculted, this provides the distnce in pixels (including binning) between the pixels to be correlted. These pixels re indicted in the imge s blue nd red frme (correltions re clculted from blue to red). Correltor P: The number of correltion chnnels for the first group of bin times. The bin time is equl to the Frme time/cquisition time. This cn bet set to 16 or 3. All following bin times will hve hlf the number of chnnels, i.e. 8 or 16. Correltor Q: This is the number of groups of bin times (including the first). The bin time within group is constnt but it will be lwys twice s lrge s the bin time of the preceding group. Exmple: Using Correltor P of 16 nd Correltor Q of 6 with Frme time of 1 ms results in the following time points for the correltion: Group 1: 1,, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 13, 14, 15, 16 Group : 18, 0,, 4, 6, 8, 30, 3 Group 3: 36, 40, 44, 48, 5, 56, 60, 64 Group 4: 7, 80 Group 5: 144, 160, Group 6: 88, ImFCS ctully lso clcultes the 0 lgtime chnnel. It is n indiction of the shot noise, but ctully it is not used in dt fitting. Fit Model: There re two choices. First there is FCS which provides fit for utocorreltion functions nd sptil cross-correltion functions. The second option is DC-FCCS nd provides dulcolour fluorescence cross-correltion fits. It is ssumed tht for DC-FCCS the imge ws split into two different wvelength rnges which were then imged onto one cmer so tht prt of the cmer contins the dt for the shorter wvelength (green) nd nother prt contins the dt for the longer wvelength (red). The distnce between the green nd red pixels hs to be provided in the CF X distnce nd CF Y distnce fields. FCCS Disply: If this is switched on (cn only be used if the DC-FCCS fit model is chosen) then both ACFs nd the CCF will be depicted. Otherwise only the CCF will be shown. Pixel Size [um]: Size of the ctul pixel on the cmer chip. This is typiclly in the rnge between 5 5 m nd cn be obtined from the cmer dtsheet. Overlp: This is toggle button to switch overlp on/off. This hs mening only when binning is used. In the cse of binning, one cn chose whether one wnts to obtin only non-overlpping pixels, or whether one wnts to hve overlpping pixels. The overlp mode cn be prcticl in sptil correltion or FCCS mesurements. Mgnifiction: Mgnifiction of the opticl system. This is required to clculte the pixel size in object spce (=pixel size/mgnifiction).

29 8 Imging FCS: A plugin for ImgeJ NA: numericl perture of the microscope objective, used to clculte the PSF. Em. Wvelength 1: Wvelength of emission, em, for the fluorophore used. This vlue is used to clculte the PSF. Em. Wvelength : (DC-FCCS only) Wvelength of emission, em, for the second fluorophore used in the cse od DC-FCCS. This vlue is used to clculte the PSF. lterl PSF (xy): This vlue, which we will cll 0, chrcterizes the 1/e rdius of the PSF in the lterl direction (long the light sheet). Which is given by 0 em/na. A typicl vlue is 0.8 (note tht in the pst we lso used the 1/e rdius which is just hlf of the 1/e rdius; so in tht cse the vlue would hve been 0.4; we decided to switch to the usge of the 1/e rdius s this is the common figure used in FCS). xil PSF (z): This vlue, which we will cll z, chrcterizes the 1/e rdius of the PSF in the xil direction (cross the light sheet), which is given by 0 em/na. To obtin good vlues the light sheet thickness needs to be mesured. If D correltion is desired, the vlue cn be set to lrge number (the defult is ) in which cse the thickness plys no role in the correltion nd essentilly D fit is performed (e.g. for imging totl internl reflection FCS or ITIR-FCS). Assuming Gussin light sheet cross section in the z-direction, the following reltions hold between the 1/e rdius () nd the full width hlf mximum (FWHM): = FWHM/ln() = 0 em/na 0 = NA*FWHM/( em * ln()) Here NA is the numericl perture of the detection objective nd em is the emission wvelength of the fluorophore observed. Note tht the observtion volume is defined by the light sheet thickness nd the pinhole effect of the pixel. Similr to the pinhole in confocl system, the pixel will detect light from different plnes differently. The user should tke ccount of this fct when providing the xil PSF (REF). lterl PSF (xy): (DC-FCCS only) Sme s bove for the second, red wvelength rnge for DC-FCCS. xil PSF (z): (DC-FCCS only) Sme s bove for the second, red wvelength rnge for DC-FCCS. Bckground: This vlue is utomticlly determined s the smllest pixel vlue in the stck to void negtive vlues. But it cn be chnged mnully. This will influence the mplitude nd thus the prmeter N in the fits. Bckground: (DC-FCCS only) This cn be djusted in cse the dt for the red chnnel hs different bckground. The defult vlue is the sme s Bckground. If the two chnnels hve different bckgrounds, then both, Bckground nd Bckground hve to be djusted mnully. Sctter: Button to perform sctter plot of fit prmters. The drop down list next to it provides the different prmeter combintions possible. Possible selections re N vs D, N vs F, D vs F,

30 9 Imging FCS: A plugin for ImgeJ N*(1-F) vs D, N*F vs D, D vs (v x +v y ) nd D vs (v x +v y ). After selection press sctter to produce sctter plot. Blech Cor.: If the intensity trces show bleching, this cn be corrected by three different methods. The different methods will sk for seprte inputs if needed. A) sliding window: by defults this divides the intensity trce in 0 smller windows of equl size (this cn be chnged in the ccompnying dilog by giving the desired window size). For ech set of frmes the correltion function is clculted nd then ll correltion functions re verged. As the intensity is not chnged the intensity trce in the Intensity Trce plot will still show the decy due to bleching. Note: if the windows re set too smll, this cn led to bised diffusion coefficients. B) single exponentil: single exponentil is fit to the intensity trce nd the trce is corrected. The corrected intensity trce will be shown in the Intensity Trce plot. C) double exponentil: double exponentil is fit to the intensity trce nd the trce is corrected. The corrected intensity trce will be shown in the Intensity Trce plot. D) polynomil fit: dilog is shown in which the order of the polynomil to be used cn be given. Typiclly one should sty with 4 or less. E) lin segment: As in sliding windo, the window size cn be set here. Within the window size the intensity is corrected for bleching by liner fits. DCCF: DCCF function which clcultes the difference of the forwrd nd bckwrd correltion fucntion. The DCCF cn be cluclted in different direction (x, y, nd digonl up or digonl down) s selected from the drop down menue next to the button. A DCCF imge nd histohrm is produced. Filter (All): One cn correlte ll pixels which fll into certin intensity rnge. This is useful if one wnts to void fitting bckground vlues, if e.g. not ll pixels in n imge contin the smple. One cn choose either to filter ccording to the intensities of the first frme in the stck ( Intensity ) or to the men vlue ( Men ) of the whole stck. This selection hs to be mde before the All button is pressed. Accompnying dilogs will sk for the limits. PSF: This will sk the user first for rnge of PSF vlues to be used (strt vlue, end vlue, step size). Typiclly one should not use more thn 5 prmeter vlues t the sme time s the clcultion cn become slow (e.g. Strt 0.7, end is 1.1, step size 0.1). The progrm will then plot the diffusion coefficients fitted by simple one component model to the smple for binning vlues from 1-5. As the diffusion coefficient is constnt the correct PSF vlue should led to stright line. Diff. lw: This will plot the FCS diffusion lw for n FCS imge. As this requires the clcultion of correltions over the whole imge severl times, this is bit slower thn e.g. fitting ll correltions in n imge. Fit on/off: The user cn decide whether fit is to be performed or not. The fits will be performed ech time correltion is done. This is used for Correlte Single, Correlte All, or when the user clicks pixel in the window. If the fit is switched on fit prmeter window is opened where strting vlues cn be given nd results re shown. In ddition new imge stck is creted in which the fit results re stored in prmeter mps. Averges for the prmeter mps re given in the title line bove the mp.

31 30 Imging FCS: A plugin for ImgeJ All : Correlte ll pixels nd plot the correltion functions. This works for uto- nd crosscorreltions nd clcultes ll possible correltions. If fit is on, then the correltions will lso be fitted. If MSD is on the MSDs will lso be clculted. Sim on/off: Provides simultor to simulte D or 3D dt with up to 3 components nd free choice of experimentl conditions. Res. Tble: Cretes or updtes the result tble with the current vlues of ll evluted dt (ACF, SD, fits etc.). Note tht the tble is not utomticlly updted. The user hs to press this button gin to updte the tble. MSD: If this button is set to MSD On then MSD is clculted long with the correltion functions nd displyed in seprte window. A dilogue will be clled when switching MSD on to determine whether D or 3D MSD clcultions re to be done. ROI : After hving chosen region of interest (ROI) pressing the button ROI will correlte ll pixels within the ROI. If fit is on, then the correltions will lso be fitted. If MSD is on the MSDs will be clculted long. To Front: Brings windows relted to this instnce of the plugin to front. This is useful for finding the windows; in prticulr in the cse tht severl instnces of the plugin re run simultneously. Experiment Sve : This button opens file dilog window in which the loction nd nme of the.xlsx file, which contins ll evlution dt, cn be chosen. Experiment Red : This button opens file dilog window in which the experimentl.xlsx file cn be chosen. Note tht to lod n experiment one hs to loded the correct imge from which the fits were produced. Exit: Closes the progrm nd ll windows, except the imge window. But it removes ll items (listeners nd overlys in jv) tht were dded to the imge window.

32 31 Imging FCS: A plugin for ImgeJ 17. Annex : Fitting Functions Note tht the full clcultions for the fitting functions hve been provided in the literture (9, 13-19) nd cn lso be obtined from interctive CDF files on our website. Therefore, we won t provide the full derivtions here. In prticulr, we left out ll clcultions of the effective volumes nd just included their results in the finl functions. The utocorreltion function G() is typiclly expressed s G g G where g() is the temporl prt of the utocorreltion function nd G is the vlue of convergence for. The vlue of G is 1 or 0 depending on the definition of the utocorreltion function (see our website here; note tht you need the CDF plugin from Wolfrm, which is freely downlodble, to see this interctive pges). It is typiclly left s fit prmeter s the condition cnnot be fulfilled. The vlue of G differs from its idel vlue usully very little, within rnge of few %. If the mplitude G(0) of the utocorreltion function G() is inversely proportionl to the number of prticles in the observtion volume, then G 0 1 G N For full derivtion see (9, 17). Therefore, we cn write G 0 1 g G Ng Below we will give the functions of g() from which g(0) nd G() cn be derived. Note tht this definition is used in ll model function in this plugin. However, it mkes strictly only sense for the temporl uto- nd cross-correltions without sptil shift. For sptil cross-correltions N is more difficult to interpret s it depends on the prticles tht pss from one re to the next nd the other prticles tht contribute to the fluorescence but not to the correltions. We provide in this plugin different generl correltion functions which cn then be modified by fixing different prmeters to obtin one nd two component models with diffusion, flow or both. The model for diffusion nd flow for one prticulr component is given by

33 3 Imging FCS: A plugin for ImgeJ g i rx vx rx vx rx vx 4D i xy 4D 4 4 i xy Di xy Di r xy x v x e e e rx vx Erf 4Di xy rx vx rx vx rx vx Erf r x vx Erf 4Di xy 4Di xy ry vy ry vy ry vy 4D i xy 4D 4 4 i xy Di xy Di r xy y v y e e e ry vy Erf 4Di xy ry vy ry vy ry vy Erf r y vy Erf 4Di xy 4Di xy 4D 1 z 1 Here the first two terms describe the diffusion nd flow in the xy directions long the pixel, nd the lst term describes the diffusion (no flow is incorported t the moment for the SPIM cse) in the z direction, orthogonl to the pixels nd cross the light sheet. The finl function for prticles, which tkes ccount of the moleculr brightness (19) is then: G 1 f g 1 g1 g g q f 0 0 N 1 f f q G Simplified models cn be obtined by setting prticulr prmeters to 0 (1, 9). A simple utocorreltion model without flow nd sptil shift, for instnce, cn be chieved by setting ll velocities v nd displcements r to 0. 1 i xy 4Di xy 1 1 4D i xy z 4D 4D gi e Erf xy xy gi 0 e 1 Erf xy nd

34 33 Imging FCS: A plugin for ImgeJ G 1 N 1 gi Ng i 0 G 1 i xy 4Di xy e 1 Erf 1 4D i xy z 4D 4D xy xy e 1Erf xy G The observtion volumes in imging FCS re given by Aeff w 0 w 0 e 1Erf w0 for ITIR-FCS, nd by V eff wz w xy w xy e 1Erf w xy for SPIM-FCS. For DC-FCCS we provide here the simplest cross-correltion function. It ssumes one diffusion coefficient nd light sheets with different size. But both light sheets re perfectly centred: G SPIM 01 w0 1 w01 w 0 4D 8D e 1 Erf 1 z z0 w 4D w w 4 1 D N w 01 w0 w01 w0 e 1Erf w01 w0 G In the plugin we llow possible shift in the light sheet direction (r z) but ssume tht the pixels for the cross-correltions re perfectly ligned. This leds to the following function (18).

35 34 Imging FCS: A plugin for ImgeJ G SPIM 01 w0 1 w 01 w0 rz 4D 8D 8D z01z0 e 1 Erf 1 e z z0 w 4D w w 4 1 D N w 01 w0 w01 w0 e 1Erf e w01 w0 r z z01z0 G The jv code for Imging FCS contins the functions for the most generl two component cses nd their derivtives for ll prmeters for dt fitting.

36 35 Imging FCS: A plugin for ImgeJ 18. Annex 3: Men Squre Displcement For the ske of simplicity for the derivtion, the following definition of the cse of SPIM-FCS G is used ignoring G. In 0 1 g G, where Ng 1 xy 4D xy 1 1 4D xy z 4D 4D g e Erf Hence G 0 1 N 1 4D eff xy 4D xy 1 1 z 4 xy z G 0 V 4D G e Erf w D G 4Dxy e 1 Erf G0V 4D 4D eff xy xy w z 4D 4D z z This eqution needs to be solved for 4D Substituting x 4D xy xy, p 1 nd z q sequentilly, we get z G G Veff Erf x x x x 0 e 1 wz q q x 4 p 4 p x e 1 Erf x coeff0 G 0, where q q x 4 p 4 p x x coeff 0 G wz 0 V eff Tylor series expnsion yielded diverging series. Hence Pde pproximtion ws used. The function used in Mthemtic is clled PdeApproximinnt. The detils of the function cn be found here ( A discussion on the effectiveness of Pde Approximtion in Mth overflow is found here (

37 36 Imging FCS: A plugin for ImgeJ pproximtion). The rticle explining Pde Approximtion in Wikipedi cn be ccessed here. ( Terms up to order 5 were needed to pproximte the function. The reltive error between the pproximtion nd the originl function is 0.7%. x e 1 Erf x Performing Pde pproximtion for q q x 4 p 4 p x x coeff x coeff x coeff x coeff x using Mthemtic, we get coeff p 16 pq 44q q p1 coeff p p q 3040 p q 3840 pq 113q 7560qp coeff coeff 3 p 40 pq 64q 63qp 1 q p p p q nd p1 15 p 0 pq q coeff x coeff coeff g x coeff x coeff coeff g x coeff g i 3 0 i 0 i 0 This polynomil in x is solved using Brent solver. The upper bound of x t t=0 is bound of x s t tends to is 0. Hence the Brent solver is progrmmed with these two limits. xy. The lower The solution obtined for x is bck trnsformed to yield 4D. This vlue is multiplied by 1.5 to yield the men squred displcement in 3D ( 6D ) since these smples re in 3D. TIRF pproximtion Similr to the SPIM cse, in the cse of TIRF, 0 1 g G where Ng xy 4D xy 4D g e 1 Erf 4D xy

38 37 Imging FCS: A plugin for ImgeJ Hence G N 4D eff xy 4D xy 1 4 xy G A G e Erf D This eqution needs to be solved for 4D Substituting x D G 4 xy x 0 A e 1 eff G Erf x e x 1 x x Erf x coeff0 G 0 Where coeff 0 G 0 Aeff Performing Tylor series expnsion of up to power 8 of e x x 1 Erf x yields x x x x The reltive error between the pproximtion nd the originl function is less thn 0.5% x x x x coeff 0 G Susbtitute t x coeff t t t t G This eqution is qurtic in t nd solver hs been implemented bsed on the lgorithm provided in IgorPro 6 (Wvemetrics ) to solve for t (solvequrtic nd getonecubicroot functions). The obtined vlues of t re lter used to clculte x which yields the vlue of x lter.

39 38 Imging FCS: A plugin for ImgeJ 19. Annex 4: Simultion The simultion module offers the opportunity to simulte different situtions nd test the results ginst rel mesurements. At the moment it offers D nd 3D simultions for ITIR-FCS nd SPIM- FCS situtions. A number of the simultion prmeters re tken from the ImFCS pnel. This includes pixel size, the NA, mgnifiction, wvelength, nd PSF nd light sheet thickness (see lterl nd xil PSF). Other prmeters cn be directly controlled in the simultion pnel. Seed: Seed for the rndom number genertor. This ensures reproducibility. Hs to be n integer. Prticle #: The number of prticles to be simulted. Hs to be n integer. CPS: Counts per Prticle nd Second; this provides mesurement for the brightness of the probes. Hs to be n integer. Blech Time: Pixel #: The pixel number n provides the dimension of the detection re (n n). At the moment only squre res re llowed. Hs to be n integer. Extension: The fctor by which the simulted re is lrger thn the detection re. Frme #: number of frmes to be simulted. Hs to be n integer. Time res: This is the frme time. D1, D, D3: diffusion coefficients in um/s of up to 3 components. F, F3: frction of the lst two components (hs to be between 0 nd 1). F1 = 1 - F - F3 Cmer offset: A constnt offset for the cmer. Cmer noise fctor: Men of Poisson Generted Noise FRAP Rdius: Only vilble in D. Rdius of circulr re to be bleched in the centre of the imge. FRAP Frme: Only vilble in D. Frme t which bleching hppens. Bleching is instntneous.